Direction of coupling from phases of interacting oscillators: An information-theoretic approach

Paluš, Milan; Stefanovska, Aneta

doi:10.1103/physreve.67.055201

Cited by 240 publications

(196 citation statements)

References 20 publications

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“…In the context of analysing instantaneous phases, Paluš & Stefanovska [61] introduced an approach based on the conditional MUI method for the detection of the direction of coupling from phases of weakly coupled oscillators. This approach is able to distinguish between uni-or bidirectional couplings and to quantify the degree of asymmetry in bidirectional coupling.…”

Section: (E) Phase Synchronizationmentioning

confidence: 99%

Cardiovascular and cardiorespiratory coupling analyses: a review

Schulz

Adochiei

Edu

et al. 2013

Phil. Trans. R. Soc. A.

145

127

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Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver–response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

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Section: (E) Phase Synchronizationmentioning

confidence: 99%

Cardiovascular and cardiorespiratory coupling analyses: a review

Schulz

Adochiei

Edu

et al. 2013

Phil. Trans. R. Soc. A.

145

127

View full text Add to dashboard Cite

show abstract

“…Many efficient methods for coupling detection have been designed [11,15,17,21,[36][37][38][39][40][41][42], and they are based around two main aspects. The first aspect is that the assessment of the strength of the interaction and its predominant direction can be used to establish if certain interactions exist at all.…”

Section: Interaction Analysis -Inverse Approachmentioning

confidence: 99%

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski

2017

Phys. Rev. E

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Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here -synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brainwaves extracted from the electroencephalography (EEG) recording of a healthy human subject in a freerunning resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions, during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions and it should be taken into account when detecting biological or other interactions from data.

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“…In these cases, we propose to test hypotheses on the basis of surrogates generated by a mathematical algorithm. Several approaches in this direction have been published (M. Palus 1997Palus , 2003. However, the specificity of these tests is not always satisfactory (Thiel et al 2006).…”

Section: Introductionmentioning

confidence: 99%

How tight is the link between lexical processing and saccade programs?

Kliegl

Engbert

2003

Behav Brain Sci

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In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.

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Direction of coupling from phases of interacting oscillators: An information-theoretic approach

Cited by 240 publications

References 20 publications

Cardiovascular and cardiorespiratory coupling analyses: a review

Cardiovascular and cardiorespiratory coupling analyses: a review

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

How tight is the link between lexical processing and saccade programs?

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